The directed acyclic graph (DAG) was used to construct the model in Netica software (Norsys Software Corp, 2019). The states were set based on literature described in Table 1 and limited to not more than five states to keep the model simple. In cases where there were more than five states, such as for the wind speed node and for wind direction, these were reduced to a maximum of five states (see [65]). A loop problem occurred when defining the network. The loop comprised light intensity, water transparency, DO epilimnion, and Chlo-a epilimnion. Actually, light intensity is directly correlated to photosynthesis capacity and reproductive ability of the algae before it is further related to the production of oxygen. As a solution to the problem, light intensity was connected directly to DO epilimnion instead of Chlo-a epilimnion to represent photosynthesis process.

A mix of data and expert domains were engaged to fill Conditional Probability Tables (CPT) referring to the work of [64]. The data to set prior probabilities were obtained from various sources (Table 1). Most ecological data (i.e., DO, Chlo-a) were obtained from measurement data of the Research Centre for Limnology-Indonesian Institute of Sciences (RCL-IIOS). Meanwhile, most daily climatic data (rainfall intensity, wind speed, wind direction, cloudy) were collected from Meteorology, Climatology, and Geophysical Agency (BMKG). The data presented in high-frequency measurement data (measured every 2 to 10 minutes) were processed into the most frequent occurrence data (i.e., wind direction, wind speed) and maximum value data (rainfall intensity).

Other CPTs (i.e., H2S, DO-metalimnion, phosphate released from sediment) were set by using expert knowledge referring to peer-reviewed publications and reports from Government Institutions. They were calibrated after conducting repeated sensitivity to parameters tests (to mixing, MFK, and Gobiopterus disappearance). Schmidt Stability Index (SSI), which shows the lake’s resistance to mechanical mixing [68] was calculated by using R-lake analyser from high-frequency measurement data from RCL-IIOS (2014–2017). The trend of SSI related to light intensity was used as the basis to fill the CPT. Detail of the method used to fill CPT of each node is presented in Table 1 and S3 Table in S1 File.

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